1. Field of the Invention
The present invention relates to a method and an apparatus for determining mean curvature of a rotating sample as well as curvature variations as a function of the rotation angle of the sample. These samples typically are semiconductor wafers with epitaxial layers grown on their surface and the apparatus is intended to be applied during the epitaxial layer deposition.
2. Description of Related Art
During epitaxial growth of semiconductor wafers the growth processes have to be monitored in dependence of different parameters as, for example, the growing layer thickness, the temperature, the doping concentration, or the smoothness of the wafer surface. Among others, an accurate measurement of the curvature of the wafer is necessary because it correlates directly with the strain in the growing layers and indirectly with the composition of these layers. In particular during epitaxial thin-film growth on wafers in multi wafer reactors it is necessary to determine permanently the curvature of the wafer as exactly as possible in the shortest possible time.
From U.S. Pat. No. 7,505,150 a device is known for the measurement of the curvature of a surface, in which a light beam is split into two parallel light beams of equal intensity by means of a birefringent element, and a two-dimensional detector is employed for determining the curvature of the surface, which is derived from the distance between the positions of the two light spots reflected at the surface to be measured and detected on the detector plane.
However, when determining the curvature of a rotating semiconductor wafer in a reactor during epitaxial growth, problems arise, due to the fact that real wafers are usually not uniformly bent, but the curvature may vary with the rotation angle, as depicted in FIG. 1, thereby leading to unwanted fluctuations in the curvature measurements. By way of example, FIG. 2 shows two signal curves measured for two samples having the same mean curvature. However, the noise/signal ratio is much higher in FIG. 2(a) than in FIG. 2(b) due to the greater rotational asymmetry of sample (a), which causes signal fluctuations between a maximum value (corresponding to L2 of FIG. 1) and a minimum value (corresponding to L1 of FIG. 1). Moreover, if the epitaxial process is not adequately controlled, defects may be generated and relaxation processes may occur in the semiconductor wafers during fabrication, which according to their symmetry may further modify the rotational asymmetry of the sample.
In particular, in the industrial production of white and blue light-emitting diodes (LEDs) on sapphire substrates, the measurement of the wafer curvature during the epitaxial growth has become a standard procedure, which is aimed to keep the curvature as small as possible by controlling the process in response to the measured curvature. In this way, it is possible to compensate for a uniform bending of the wafers, but not for an asymmetrical bending, which represents one of the principal causes reducing the rate of yield.
It is therefore an object of the present invention to provide a method and an apparatus for a real-time determination of the curvature of a rotating sample with a higher accuracy in comparison to the prior art. In particular, a high noise/signal ratio of the measured signal due to a rotating sample having an azimuthal asymmetry of the curvature shall be effectively suppressed.
It is a further object of the present invention to effectively determine a film relaxation of the sample and/or the formation of defects on the sample, thus providing important parameters for controlling the fabrication process.